Competition of Steric Repulsion and Electrostatic Attraction in Model Calcium Channels

1. Calcium channels conduct Na ions in the absence of Ca2+, but they selectively conduct Ca2+ ions when Ca2+ ions are present at physiological concentrations. In the anomalous mole fraction effect (AMFE), even a micromolar amount of Ca2+ ions effectively blocks Na current. Many attempts have been made to explain the mechanism behind these phenomena. In our model of the selectivity filter of Ca channels, the end-groups of the side chains of amino acids - four glutamates - in the selectivity filter are represented as mobile ions that are restricted so they move inside the filter. These structural ions form a liquid-like self-adjusting environment for the passing ions so that the system assumes minimum free energy. They also fill part of the pore so the counterions have to compete for space in the crowded selectivity filter. In this picture electrostatic attraction and repulsive entropic excluded volume effects compete with each other to determine which ions can enter the selectivity filter. We argue that this competition is crucial in explaining the selectivity mechanism of Ca channels. We show Monte Carlo simulation results for competition between ions of different valence and diameter. We predict that Ca2+-selectivity depends on the background concentration of NaCl. We show that our model can explain the micromolar Ca2+-selectivity observed in the L-type Ca channel. We also show results for an alternative model of Ca2+ channels developed by Corry et al. In this model, the structural ions are placed in fixed positions behind the protein wall. We show that this rigid model cannot reproduce the micromolar selectivity of the L-type Ca channel. Competition of Steric Repulsion and Electrostatic Attraction in Model Calcium Channels Dezső Boda1,2, Wolfgang Nonner3, Mónika Valiskó2, Douglas Henderson4, Bob Eisenberg1, Dirk Gillespie1 1Rush University Medical Center, Chicago, IL; 2University of Pannonia, Veszprém, Hungary; 3Miller School of Medicine University of Miami, Miami, FL; 4Brigham Young University, Provo, UT Abstract CSC model has micromolar Ca2+ selectivity Size selectivity: Ca2+ vs. Ba2+ AMFE • DCa/DNa ratios adjusted to experi- mental values at xCa=1. • Experiments: • Friel and Tsien,PNAS, 1989, 86: 5107. DCa/DNa=0.280 • Yue and Marban, JGP,1990, 95: 911. DCa/DNa=0.214 Ca2+-selectivity depends on NaCl concentration: As [NaCl] increases, Ca2+-affinity decreases. AMFE is a result of different concentration dependence in the high affinity central region of the filter (-2.5 < z < 2.5) and in the depletion regions (2.5 < |z| < 5). For details, see neighboring poster 2221-POS/B336. The CSC model Theory vs. Experiments The Charge Space Competition (CSC) model states that cations are attracted into the selectivity filter by charged amino acids making for a very crowded filter where it is difficult for ions to find space. This competition of energy and entropy favors small and/or divalent ions in the crowded filter because they provide more chargein less space to balance the charge of the structural ions of the selectivity filter. Concentration profiles of Ca2+ and Ba2+ along the pore for various Ca2+ mole fractions xCa=[Ca2+]/ctotal., where the total concentration is kept fixed at ctotal=10 mM. Occupancy curves of Ca2+ and Ba2+ and normalized currents for two experiments. One group found an AMFE, one group did not. We reproduce both results. Occupancy of Na+ in the selectivity filter is a measure of the Ca2+-block of Na+ current because they are strongly correlated. Concentration profiles of Ca2+ and Na+ along the pore for various [NaCl]. In the CSC model there is lots of Ca2+ in the selectivity filter at micromolar [CaCl2]. Occupancy curves of Ca2+ and Na+ and normalized currents for various [NaCl]. X symbols are the experimental data of Almers et al. (J. Physiol. 353: 565) for 32 mM NaCl. • Channel: a doughnut shaped object with a pore in the middle with proteindielectric coefficiente=10 and pore radiusR=3.5Å. • It is embedded in a membrane that separates two baths. • Ions: charged hard spheres, solvent: continuum dielectric (εw = 80)‏ • Selectivity filter: central pore containing characteristic amino acid side chains: hard sphere ions model the terminal groups of the side chains: E: two half charged oxygens (O1/2-, red balls in figures to the left). The Ca channel model of Corry et al. is only weakly Ca2+-selective Loss of Ca2+ selectivity in E A mutations • Squares and solid lines: results of direct Brownian Dynamics simulations • Dashed and dotted lines: results of extrapolations • X: Experimental data of Almers et al. Concentration profiles of Ca2+ and Na+ along the pore for mutations for [CaCl2] = 86 mM and [NaCl] = 100 mM. Occupancy curves of Ca2+ and Na2+ and normalized currents for various mutations. • They simulated >18 mM Ca2+, and extrapolated four orders of magnitude to micromolar concentrations. • We directly simulated micromolar Ca2+ concentrations and showed that the Corry et al. model has >100 mM Ca2+-affinity, not 1 mM. • We showed that placing structural ions in the selectivity filter of the Corry et al. model, micromolar Ca2+ selectivity is restored. • This indicates that the excluded volume of the ions is important. The Ca channel model of Corry et al. (Biophys. J. 2001, 80: 195)‏ • Mutating the negatively charged E into the neutral and small A, the Ca2+-affinity of the channel decreases. • The Ca2+ block of Na+ currents occurs at higher Ca2+ concentration for EEEA. • In the weakly charged filter (EEAA) there is no Ca2+ block because no depletions regions for Ca2+ form. • The Corry et al. model contains • a narrow selectivity filter surrounded by structural charges in fixed positions behind the wall (red balls in the figure), • a large cavity that imposes a dielectric barrier, • dipoles at the intracellular entrance (yellow and blue balls in the figure)‏ Axial distributions of Ca2+ and Na+ along the pore for different Ca2+ concentrations. In the Corry et al. model there is almostnoCa2+ in the filter at micromolar Ca2+ concentration. Upper panel: the extrapolated results of Corry et al. Bottom panel: Occupancy curves of Ca2+ and Na+ as obtained from GCMC simulations. Methods • Equilibrium profiles are computed with Grand Canonical Monte Carlosimulations (micromolar Ca2+ concentrations can be simulated directly). • Normalized currents are computed by substituting these profiles into the integrated Nernst- Planck equation with the assumptions that the electrolytes are symmetric on the two sides of the membrane, voltage is small, and that flux is limited in the selectivity filter. • The adjustable parameter of this calculation is the ratio of the diffusion coefficients of the two ions (for example, DCa/DNa=0.1 was used here). • For details, see neighboring poster 2221-POS/B336. Conclusions References • Selectivity is a result of the balance of electrostatic forces (energy) and excluded volume of ions (entropy). • The mobileterminal groups of protein side chains have a close interaction with ions: they form a liquid-likeflexibleenvironment that is more similar to an ionic liquid than to a dilute electrolyte solution. • The CSC model reproduces experimental results and makes predictions (experiments are needed). • A large range of phenomena is explained using only basicphysical forces and robust,reproducible methods. • CSC model: Nonner, W., Catacuzzeno, L., and B. Eisenberg. 2000. Biophys. J. 79:1976. • Effect of protein dielectric coefficient and pore radius:Boda et al., 2006, J. Chem. Phys. 125: 034901;Boda et al., 2007. Phys. Rev. Lett. 98:168102. • Application to Na channels: Boda et al. 2007, Biophys. J. 93: 1960. • Application to the model of Corry et al.: Boda et al. 2008, Biophys. J. in press, doi:10.1529/biophysj.107.122796